ON An Infra-\(\alpha\)-Open Sets

Abstract

In this paper, we define a new class of set in general topology called an infra-α-open set and we investigate fundamental properties by using this new class. The relation between infra-α-open set and other topological sets are studied. Moreover, In the light of this new definition, we also define some generalization of continuous mappings and discuss the relations between these new classes of mappings and other continuous mappings. Basic properties of these new mappings are studied and we apply these new classes to give characterization of connected space.

Infra − β − Closed(Open) Sets : New

“…(ii) Interior * (φ) [20] ( resp. inf ra−β −closed [20], inf ra − pre − open [20], inf rasemi open [22] and inf ra − α − open [17] )…”

Weak and strong forms of fuzzy \(\alpha\)-open (closed) sets and its applications

“…(4) Fuzzy supra-semicontinuous (resp. infra-semicontinuous) [8] if f −1 (ϕ) is a fuzzy supra-semiopen (supra-semiclosed) resp. infra-semiopen (infra-semiclosed) set in X for each fuzzy open (closed) set ϕ in Y.…”

“…In 2013, Missier and Rodrigo introduced new class of set called a α * -open (supra-α-open) set and in 2016, Othman and Page, [8] have introduced the concept of infra-α-open sets in general topology. In this paper, we generalize all result of these two papers research and more interesting results on these new concepts and we also apply these new concepts in order to introduce some kinds of mappings.…”